Newtons Law of cooling problem

[Joe!]

(my teacher had posted this question for our class to solve, but I'm not sure how i get this answer, I pasted the thing he sent us so it will be as specific as it can get.)
Thank you for any help I can get! -With love, Joe

This is a situation that happened to me on December 9th... no seriously... a real situation. Here it is.

I got some coffee and (yes I had a thermometer on him) and I measured it at 7:03 pm and it was 140 degrees. The waiter mentioned that it was boiling hot just a few
minutes ago and that he hurried it to me. Is the waiter lying? Should I give him an extra big tip? Maybe... but my question is... at what time did the coffee stop boiling and so how long did he take to bring it to me? (Please be specific! I need this to be down to the hour, minute, and second if possible.)

this requires that you solve k in the formula for Newton's Law of Cooling BEFORE you can figure out time, so this is a two-part problem. After you calculate k, THEN you can use it in the specific equation to calculate how long it took for him to bring me the coffee. Here are the specifics.

Room Temperature = 72 degrees
Coffee Temperature at 7:03 pm = 140 degrees
Coffee Temperature at 7:10 pm = 90 degrees (yes I did wait 10 minutes to measure it so I could calculate k)
Boiling point of water = 212 degrees

You will need Newton's Law of Cooling.

 

[Deleted member 4993]

(my teacher had posted this question for our class to solve, but I'm not sure how i get this answer, I pasted the thing he sent us so it will be as specific as it can get.)
Thank you for any help I can get! -With love, Joe

This is a situation that happened to me on December 9th... no seriously... a real situation. Here it is.

I got some coffee and (yes I had a thermometer on him) and I measured it at 7:03 pm and it was 140 degrees. The waiter mentioned that it was boiling hot just a few
minutes ago and that he hurried it to me. Is the waiter lying? Should I give him an extra big tip? Maybe... but my question is... at what time did the coffee stop boiling and so how long did he take to bring it to me? (Please be specific! I need this to be down to the hour, minute, and second if possible.)

this requires that you solve k in the formula for Newton's Law of Cooling BEFORE you can figure out time, so this is a two-part problem. After you calculate k, THEN you can use it in the specific equation to calculate how long it took for him to bring me the coffee. Here are the specifics.

Room Temperature = 72 degrees
Coffee Temperature at 7:03 pm = 140 degrees
Coffee Temperature at 7:10 pm = 90 degrees (yes I did wait 10 minutes to measure it so I could calculate k)
Boiling point of water = 212 degrees

You will need Newton's Law of Cooling.

Do you know the mathematical description of Newton's Law of cooling?

If you do not - please review your class-notes/text book or search Google.

If you do - please tell us what it is?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Joe!]

Do you know the mathematical description of Newton's Law of cooling?

If you do not - please review your class-notes/text book or search Google.

If you do - please tell us what it is?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

Newtons law of cooling states that “the rate of heat loss of a body is proportional to the difference in the temperatures between the body and its surroundings”, and the formula for it would be
T(t) = Ta+(T0-Ta)e^-kt.
And i have ended up with this,
T(t)= 72+(?-72)e^-k?
I am seriously just confused on:
-If i use the boiling point of water or 140 for initial temp and t
-how i would initially get k
-How i would recheck if my final solution is correct.

 

[skeeter]

the boiling point of water is a distracting value ...

let [MATH]t=0[/MATH] be at 7:03 [MATH]\implies T(0) = 140 \text{ and } T(7) = 90[/MATH]
[MATH]140 = 72 + (140-72) \cdot e^{-k \cdot 0}[/MATH]
[MATH]90 = 72 + 68e^{-k \cdot 7}[/MATH]
solve for k